Details

Time bar (total: 12.2s)

sample76.0ms

Algorithm
intervals
Results
41.0ms96×body1280valid
16.0ms65×body640valid
4.0ms68×body80valid
3.0ms16×body320valid
1.0ms11×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089
1129
2169
3199
4209
done209

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(* r (sin b))
0.2b
(/ (* r (sin b)) (cos (+ a b)))
3.4b
(cos (+ a b))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1
3×expm1-log1p-u times-frac associate-*r* associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×cos-sum frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 53
Calls
3 calls:
4.0ms
(* r (sin b))
4.0ms
(/ (* r (sin b)) (cos (+ a b)))
7.0ms
(cos (+ a b))

series158.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* r (sin b))
96.0ms
(/ (* r (sin b)) (cos (+ a b)))
24.0ms
(cos (+ a b))

simplify1.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (453.0ms)

IterNodesCost
096575
1208562
2581484
32300482
done5000482

prune164.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.1b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(* (sin a) (sin b))
0.2b
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×sin-mult
4×expm1-log1p-u associate-/r/ cos-mult log1p-expm1-u
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative frac-sub flip-- sub-div unswap-sqr
1×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
3.0ms
(* r (sin b))
8.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms
(* (sin a) (sin b))
9.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* r (sin b))
76.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms
(* (sin a) (sin b))
208.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.3s

Counts
98 → 98
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01521364
13661324
211611268
344151081
done50001080

prune343.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin b) (sin a))
0.2b
(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
0.3b
(* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
0.4b
(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-cbrt-cube
18×add-sqr-sqrt
16×times-frac
14×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv div-exp
10×associate-/r*
8×pow1 prod-exp cbrt-unprod
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative fma-udef associate-/l* unswap-sqr
1×distribute-rgt-in distribute-lft-in associate-/r/ sin-mult
Counts
4 → 106
Calls
4 calls:
4.0ms
(* (sin b) (sin a))
7.0ms
(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
3.0ms
(* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
4.0ms
(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin b) (sin a))
215.0ms
(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
168.0ms
(* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
86.0ms
(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a))))

simplify1.3s

Counts
118 → 118
Iterations

Useful iterations: 2 (420.0ms)

IterNodesCost
01914205
14864164
223312271
done50002271

prune454.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin b) (sin a))
0.2b
(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
0.3b
(* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
0.4b
(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log add-cbrt-cube
18×add-sqr-sqrt
16×times-frac
14×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv div-exp
10×associate-/r*
8×pow1 prod-exp cbrt-unprod
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative fma-udef associate-/l* unswap-sqr
1×distribute-rgt-in distribute-lft-in associate-/r/ sin-mult
Counts
4 → 106
Calls
4 calls:
4.0ms
(* (sin b) (sin a))
6.0ms
(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
3.0ms
(* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
4.0ms
(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a))))

series511.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin b) (sin a))
216.0ms
(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a)))))
168.0ms
(* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
84.0ms
(/ (* (fma (cos a) (cos b) (* (sin b) (sin a))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin b) (sin a))))

simplify1.3s

Counts
118 → 118
Iterations

Useful iterations: 2 (418.0ms)

IterNodesCost
01914205
14864164
223312271
done50002271

prune400.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01740
12738
22938
done2938

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.4s2916×body1280valid
475.0ms1853×body640valid
136.0ms737×body320valid
127.0ms2155×body80valid
43.0ms341×body160valid